Mathematics

Grade10

Easy

Question

# The two sides of the right triangle are 12 units and 16 units, what will be length of third large side by using quadratic square roots?

- 7
- 11
- 9
- 8

Hint:

### In this question , two sides of the right angled triangle is given , they are 12 unit and 16 unit . find third largest side by using quadratic square roots . Use formula for hypotenuse in right triangle.

## The correct answer is: 9

### Here we have to find the third largest side of right triangle.

Firstly , we have two side which is 12 unit and 16 unit.

Let the three sides be a, b and c .

Then a = 12 unit , b = 16 unit and c =?(Let x)

We have formula for hypotenuse,

(x)^{2} = (a)^{2} + (b)^{2}

(x)^{2} = 144 + 256

(x)^{2} = 400

Taking square root on both the sides of the equation, we get

Since the length of the side cannot be negative, x= 20 units

In this question, we have given two sides which is 12 and 16 and we have to find the third side which is large. So we have formula for hypotenuse which is c^{2 }=a^{2 }+b^{2} but hypotenuse is largest side of the right triangle so for smaller side we can write this formula as b^{2} = c^{2} – a^{2} , here we used property of equality to find this formula.